Could you please try to find the intersections points of this two functions: $ y = x $ and $y=(a+x) \ {\rm e}^ {-2(a+x)} $ with $x\geq0$
Thanks for your help
5
-
1$\begingroup$ Hi Ivan, Welcome to MSE! Can you please post the code you have tried. $\endgroup$– Rohit NamjoshiSep 26, 2019 at 14:50
-
2$\begingroup$ Try the Lambert function en.wikipedia.org/wiki/Lambert_W_function $\endgroup$– yarchikSep 26, 2019 at 14:55
-
$\begingroup$ see also ProductLog $\endgroup$– kglrSep 26, 2019 at 15:04
-
2$\begingroup$ The generalization of the Lambert function by Mező real.mtak.hu/39795/1/… is relevant $\endgroup$– yarchikSep 26, 2019 at 15:13
-
$\begingroup$ @yarchik Looks amazing. $\endgroup$– Chris DegnenSep 27, 2019 at 11:05
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
To visualize the pairs of real numbers {x, a} that satisfy the equation,
you can use ContourPlot:
ContourPlot[(a + x) E^(-2 (a + x)) == x, {x, -2, 1}, {a, 0, 5}]
or RegionPlot with options MeshFunctions + Mesh:
RegionPlot[True, {x, -2, 1}, {a, 0, 5},
BoundaryStyle -> None,
MeshFunctions -> {(#2 + #) E^(-2 (#2 + #)) - # &},
Mesh -> {{0}},
MeshStyle -> Directive[Thick, Red],
PlotStyle -> None,
PlotPoints -> 100]
$\begingroup$
$\endgroup$
Looks like you'll need some constraints on a.
a = -1;
f[x_] := (a + x) E^(-2 (a + x))
Plot[{x, f[x]}, {x, 0.001, 4}, PlotRange -> {Automatic, {-2, 1}}]
answered Sep 26, 2019 at 14:56